Internal problem ID [11842]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=\frac {1}{{\mathrm e}^{2 x}+1}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 38
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=1/(1+exp(2*x)),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (\ln \left ({\mathrm e}^{2 x}+1\right ) {\mathrm e}^{-x}+2 c_{1} {\mathrm e}^{-x}-2 \arctan \left ({\mathrm e}^{x}\right )-2 c_{2} \right ) {\mathrm e}^{-x}}{2} \]
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 45
DSolve[y''[x]+3*y'[x]+2*y[x]==1/(1+Exp[2*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-2 x} \left (2 e^x \arctan \left (e^x\right )-\log \left (e^{2 x}+1\right )+2 \left (c_2 e^x+c_1\right )\right ) \]